Simulation ofCommunication Systems Second EditionInformation Technology: Transmission, Processing, and StorageSeries Editor: Jack Keil WolfUniversity of California at San DiegoLa Jolla, CaliforniaEditorial Board: James E. MazoBell Laboratories, Lucent TechnologiesMurray Hill, New JerseyJohn ProakisNortheastern UniversityBoston, MassachusettsWilliam H. TranterVirginia Polytechnic Institute and State UniversityBlacksburg, VirginiaMulti-Carrier Digital Communications: Theory and Applications of OFDMAhmad R. S. Bahai and Burton R. SaltzbergPrinciples of Digital Transmission: With Wireless ApplicationsSergio Benedetto and Ezio BiglieriSimulation of Communication Systems, Second Edition: Methodology,Modeling, and TechniquesMichel C. Jeruchim, Philip Balaban, and K. Sam ShanmuganA Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volumeimmediately upon publication. Volumes are billed only upon actual shipment. For further information please contactthe publisher.Simulation ofCommunication Systems Second EditionModeling, Methodology, and TechniquesMichel C. JeruchimLockheed Martin Management & Data SystemsValley Forge, PennsylvaniaPhilip BalabanAT&T LaboratoriesHolmdel, New JerseyK. Sam ShanmuganUniversity of KansasLawrence, KansasKLUWER ACADEMIC PUBLISHERSNEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOWeBook SBN: 0-306-46971-5Print SBN: 0-306-46267-22002 Kluwer Academic PublishersNew York, Boston, Dordrecht, London, MoscowPrint 2000 Kluwer Academic / Plenum PublishersNew YorkAll rights reservedNo part of this eBook may be reproduced or transmitted in any form or by any means, electronic,mechanical, recording, or otherwise, without written consent from the PublisherCreated in the United States of AmericaVisit Kluwer Online at: http://kluweronline.comand Kluwer's eBookstore at: http://ebooks.kluweronline.comToJoan, Claude, and Kennyand to the memory of my parents, Sonia and SamuelMCJAnna, to Victor and Nona and their familiesand to the memory of my parents, Shifra and IsraelPBRadha, Kannon, and Raviand to the memory of my parentsKSS7KLVSDJHLQWHQWLRQDOO\OHIWEODQNPrefaceSince the first edition of the book was published, the field of modeling and simulation ofcommunication systems has grown and matured in many ways, and the use of simulation as aday-to-day tool is now even more common practice. Many new modeling and simulationapproaches have been developed in the recent years, many more commercial simulationpackages are available, and the evolution of powerful general mathematical applicationspackages has provided still more options for computer-aided design and analysis. With thecurrent interest in digital mobile communications, a primary area of application of modelingand simulation is now to wireless systems of a different flavor than the traditional ones.Since the objective of modeling and simulation is to study and evaluate the behavior andperformance of systems of current interest, the practice of simulation has naturally evolvedalong with the types of systems that have emerged or are being designed for the future.Nevertheless, to the extent that simulation is an embodiment of fundamental principles ofseveral disciplines, communication theory in particular, the practice of modeling and simu-lation is still very much grounded in those basics. It is these principles, along with the manytricks of the trade that accompany their application, that still form the main focus of thissecond edition.This edition represents a substantial revision of the first, partly to accommodate the newapplications that have arisen. The text has been extensively reorganized and expanded. It nowcontains 13 chapters instead of the previous 7. Some of the former chapters have been dividedinto more logical units, edited for greater clarity where needed, and extended in coverage forselected topics. This division was made in part to facilitate the use of this book as a teachingtext. Two new chapters were added on material only lightly covered in the first edition. Onenew chapter, on modeling and simulation of nonlinear systems, provides a fairly extensivediscussion of black-box modeling of nonlinear systems with memory, and a comple-mentary section on related measurement techniques. As hinted above, perhaps the mostdramatic change in the communications/telecommunications industry since the first editionhas been the explosion of wireless services. In consequence, we have included a new chapteron channel modeling, the bulk of which deals with multipath and fading channels, the usualenvironment for wireless systems. As in the first edition, one chapter provides several casestudies as a means of illustrating different ways of approaching a problem and applyingspecific modeling and computational techniques from the arsenal of possibilities available tothe simulation practitioner. The first case study is a thoroughly reworked version of a previousviiviii Prefaceone, and three new case studies are given. A consolidated set of problems can be foundfollowing Chapter 12.By their nature, simulation and modeling embrace the whole of the fields to which theyare applied. To cover such a breadth of material, even larger now than in the first edition, wehave had again to rely on the generosity of friends and colleagues to provide us with adviceand material on various topics. First, we would like to reacknowledge the contributors to thefirst edition, whose contributions by and large still live in these pages.For the second edition, the list has grown longer. To our good friend and colleague atLockheed Martin M&DS, Dr. Robert J. Wolfe, mathematician and statistician par excellence,we extend our gratitude for innumerable pieces of advice, proofs, and inputs on coding,nonlinear differential equations, random number generation, and interpolation, among others.Dr Wolfe also reviewed several chapters and provided the basic material for the section onlarge-deviations theory (Section 11.2.5.3.2). Numerous contributions were also made by othermembers of the Communications Analysis and Simulation Group at Lockheed MartinM&DS. Aside from Bob Wolfes work just mentioned, Douglas Castor and Dr. GregoryMaskarinec kindly made available their previously published work on minimum-shift-keying,which was edited into Case Study III in Chapter 12. In addition, Doug generated all thefigures and carefully reviewed the final manuscript for that case study. We also benefited frommany discussions with Dr. Maskarinec about nonlinear modeling, based on his extensivesurvey of the literature; Greg also reviewed Chapter 5 and contributed the model in Section5.3.4.2. We appreciate the efforts of Gregory Sternberg, who used his expertise in Mathe-matica to compute Table 11.1 and to generate Figures 11.23 and 11.24. We thank PaulBeauvilliers for using his experience in simulating phase-locked loops to produce the materialfor Example 8.12.2 and the associated figures. We also express our appreciation to DanielMcGahey, who supplied the block diagram, its details, and the timing information that formthe basis for the discussion in Section 11.2.1.The team of Dr. Christopher Silva, Christopher Clark, Dr. Andrew Moulthrop, andMichael Muha at Aerospace Corporation were most generous in lending us the benefit of theirexperience and knowledge in nonlinear system modeling and measurement. The teamsupplied Section 5.5 on measurement techniques for nonlinear components. Dr. Silva wentbeyond the call of duty by providing the material on generalized Volterra models and poly-spectral models in Section 5.3.3, as well as the material in Section 5.2.4.3, supplying severalof the related problems, and thoroughly reviewing Chapter 5. Chris Clark is also to bethanked individually for writing Section 5.3.4.2 on nonlinear parametric discrete-timemodels. We have also benefited from numerous discussions with Harvey Berger of TRW onhis published and unpublished work in nonlinear amplifier modeling.Several individuals presently or formerly at AT&T Laboratories, or formerly with BellLaboratories, made contributions that we would like to acknowledge. Our appreciation isextended to Dr. William Turin, who codeveloped and coauthored Case Study IV in Chapter12; Bill also kindly reviewed sections of the book dealing with Markov models. We also thankDr. Don Li for his contributions as a codeveloper of the material in Case Study IV We aremost grateful to Dr. Thomas M. Willis III for contributing the material on shadow fading inChapter 9. We also express our gratitude to Dr. Seong (Sam) Kim for providing the materialand the figures on indoor channel modeling in Chapter 9. We also acknowledge manydiscussions with Dr. Zoran Kostic on the workings of code division multiple-access (CDMA)systems; his advice helped shape Case Study IVWe are indebted to Prof. Irving Kalet of the Technion, Haifa, Israel, for providing thematerial (and its iterations) on orthogonal frequency division multiplexing (OFDM) thatPreface ixappears in Section 8.7.2.2. We much appreciate the efforts of Prof. J. Keith Townsend ofNorth Carolina State University for many discussions on importance sampling, for inputs intoSection 11.2.5.4 on stochastic importance sampling, and for the whole of Section 11.2.6 onimportance splitting. Keith also made other materials available that could not be accom-modated for space reasons. We thank Dr. Faroukh Abrishamkar of Qualcomm for his adviceon CDMA system modeling and for providing some of the reference channel models in theAppendix to Chapter 9. Professor Vasant Prabhu of the University of Texas at Arlington wasmost kind to provide us with several problems that he uses for his course in simulation, andlikewise we are pleased to acknowledge Prof. Brian Woerner of Virginia Polytechnic Institutefor providing us with a number of projects following Chapter 12.Finally, we renew our acknowledgment to our families for bearing with usa secondtimethrough this long process.Michel C. JeruchimPhilip BalabanK. Sam Shanmugan7KLVSDJHLQWHQWLRQDOO\OHIWEODQNContentsChapter 1. Introduction1.1.1.2.1.3.1.4.1.5.Methods of Performance Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.1.1.1.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hierarchical View. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation Approach: Waveform-Level Simulation of Communication Systems. . . . . .The Application of Simulation to the Design of Communication Systems . . . . . . . . .Historical Perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Outline of the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 2. Simulation and Modeling Methodology2.1.2.2.2.3.Some General Remarks on Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Methodology of Problem Solving for Simulation . . . . . . . . . . . . . . . . . . . . . . . .Basic Concepts of Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.1.2.3.2.2.3.3.2.3.4.2.3.5.System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Device Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Random Process Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Modeling Hypothetical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation with Hardware in the Loop . . . . . . . . . . . . . . . . . . . . . . . . .2.4.2.5.Performance Evaluation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Error Sources in Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.5.1.2.5.2.2.5.3.2.5.4.Errors in System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Errors in Device Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Errors in Random Process Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . .Processing Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6. Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6.1.2.6.2.2.6.3.Validating Models of Devices or Subsystems . . . . . . . . . . . . . . . . . . . . .Validating Random Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . .Validating the System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7. Simulation Environment and Software Issues . . . . . . . . . . . . . . . . . . . . . . . . . .2.7.1.2.7.2.2.7.3.2.7.4.Features of the Software Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Components of the Software Environment . . . . . . . . . . . . . . . . . . . . . . .Hardware Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi1123568121416172121222325262830313235363738394142434545Contents2.8.2.9.The Role of Simulation in Communication System Engineering . . . . . . . . . . . . . . .Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 3. Representation of Signals and Systems in Simulation: AnalyticFundamentals3.1.3.2.3.3.3.4.3.5.Introduction to Deterministic Signals and Systems . . . . . . . . . . . . . . . . . . . . . . .3.1.1.3.1.2.3.1.3.Continuous Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Discrete-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.1.3.1.3.1.3.2.Properties of Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Block Diagram Representation of Systems . . . . . . . . . . . . . . . . .Linear Time-Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.1. Continuous Linear Time-Invariant Systems. . . . . . . . . . . . . . . . . . . . . . . . . .3.2.1.1.3.2.1.2.The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Convolution Integral, . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.2. Discrete Linear Time-Invariant Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.2.1.3.2.2.2.The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Convolution Sum (Discrete Convolution) . . . . . . . . . . . . . . . . . . . . . .Frequency-Domain Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.1. The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.1.1.3.3.1.2.The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Convolution Integral. . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.2. Frequency-Domain Representation of Periodic Continuous Signals. . . . . . . . .3.3.2.1.3.3.2.2.The Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Parsevals Theorem for Periodic Signals. . . . . . . . . . . . . . . . . . . . . . .3.3.3. The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.3.1.3.3.3.2.Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . .3.3.4. The Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.4.1.3.3.4.2.Interconnection of Systems in the Frequency Domain . . . . . . . . . .Parsevals Theorem for Continuous Signals. . . . . . . . . . . . . . . . . . . .3.3.5.3.3.6.3.3.7.The Gibbs Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Relationship between the Fourier Transform and the Fourier Series . . . . . . . .3.3.6.1.3.3.6.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Fourier Series Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Fourier Transform of a Periodic Signal . . . . . . . . . . . . . . . . . . . . . .3.3.7.1.3.3.7.2.Periodic Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Poisson Sum Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Lowpass-Equivalent Signals and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4.1.3.4.2.3.4.3.3.4.4.3.4.5.The Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Properties of the Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . .Lowpass-Equivalent Modulated Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . .Hilbert Transform in System Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4.4.1.3.4.4.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Lowpass Equivalent of a Bandpass Filter . . . . . . . . . . . . . . . . . .Practical Considerations in Modeling of Lowpass Equivalents for Simulation. . .3.4.5.1.3.4.5.2.Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sampling and Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4952545656575959606162626262626363636262656566666767707070717272727273747475777879797982828383xiiContents xiii3.5.1.3.5.2.3.5.3.3.5.4.Impulse Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sampling Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multirate Sampling and Sampling Conversion . . . . . . . . . . . . . . . . . . . . .Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.5.4.1.3.5.4.2.3.5.4.3.3.5.4.4.3.5.4.5.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Interpolator Structures for Integer Upconversion. . . . . . . . . . . . . . . . . . .Bandlimited and Windowed Bandlimited Interpolation . . . . . . . . . .Linear Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Spline Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.6.3.7.3.8.3.9.3.10.Characterization of Linear Time-Invariant Systems Using the Laplace Transform. . . . .3.6.1.3.6.2.3.6.3.3.6.4.3.6.5.3.6.6.The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.6.1.1.3.6.1.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Convergence and Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Inverse Laplace Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Properties of the Laplace Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Transfer or System Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Interconnections of LTI Systems (Block Diagrams) . . . . . . . . . . . . . . . . . . . . .Systems Characterized by Linear Constant-Coefficient Differential Equations. . .3.6.6.1.3.6.6.2.Properties of the Transfer Function for Linear Constant-CoefficientDifferential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Realizations of Rational Transfer Functions Using BiquadraticExpansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.6.7. Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Representation of Continuous Systems by Discrete Transfer Functions . . . . . . . . . . .3.7.1. The z-Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.7.1.1.3.7.1.2.3.7.1.3.3.7.1.4.Convergence and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . .Table of Simple z-Transforms . . . . . . . . . . . . . . . . . . . . . . . . .Properties of the z-Transform . . . . . . . . . . . . . . . . . . . . . . . . .Discrete Transfer or System Function . . . . . . . . . . . . . . . . . . . .Fourier Analysis for Discrete-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . .3.8.1.3.8.2.3.8.3.3.8.4.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Properties of the Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . .3.8.4.1.3.8.4.2.3.8.4.3.3.8.4.4.3.8.4.5.3.8.4.6.3.8.4.7.3.8.4.8.Periodic or Circular Properties . . . . . . . . . . . . . . . . . . . . . . . .The Periodic Time-Shift Property. . . . . . . . . . . . . . . . . . . . . . .The Periodic or Circular Convolution . . . . . . . . . . . . . . . . . . . .The Discrete Periodic Convolution Theorem . . . . . . . . . . . . . . . .The Discrete Frequency Response . . . . . . . . . . . . . . . . . . . . . .Relationship between the Bandwidth and the Duration of theImpulse Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Relationship between the Discrete Fourier Transform and thez-Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Increasing the Frequency Resolution of the Discrete FourierTransform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Appendix: A Brief Summary of Some Transforms and Theorems Useful inSimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8386878990939698100106106106106107107108108110111112114115115116117117117118118119120121121122123124124124125125126127131xiv ContentsChapter 4. Modeling and Simulation of Linear Time-Invariant andTime-Varying Systems4.1. Modeling and Simulation of Linear Time-Invariant Systems . . . . . . . . . . . . . . . . .4.1.1.4.1.2.4.1.3.4.1.4.LTI Filters: Description, Specification, and Approximation . . . . . . . . . . . . .4.1.1.1.4.1.1.2.4.1.1.3.4.1.1.4.4.1.1.5.4.1.1.6.Filter Descriptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Continuous Classical Filters . . . . . . . . . . . . . . . . . . . . . . . . . .Frequency Transformations . . . . . . . . . . . . . . . . . . . . . . . . . .Lowpass Equivalents of Bandpass Filters Represented by RationalFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Filter Specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Approximating Continuous Structures in Discrete Time forSimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation of Filtering with Finite Impulse Response Filters . . . . . . . . . . . .4.1.2.1.4.1.2.2.4.1.2.3.4.1.2.4.Simulation of FIR Filtering in the Time Domain . . . . . . . . . . . . .4.1.2.1.1.4.1.2.1.2.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .Windowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation of FIR Filtering in the Frequency Domain . . . . . . . . . .4.1.2.2.1.4.1.2.2.2.4.1.2.2.3.4.1.2.2.4.4.1.2.2.5.4.1.2.2.6.Difference between Periodic and Linear Convolution....Linear Convolution for a Signal of Arbitrary Durationvia the FFT. . . . . . . . . . . . . . . . . . . . . . . . . . .The Overlap-and-Add (OA) Method. . . . . . . . . . . . . . . . .The Overlap-and-Save (OS) Method. . . . . . . . . . . . . . . . .Efficiency of the Linear Convolution via the FFT. . . . . . . .Implications of Frequency-Domain FIR Filtering . . . . . .Mapping of Continuous Filters into Discrete FIR Filters . . . . . . . . .4.1.2.3.1.4.1.2.3.2.FIR Filters Defined in the Time Domain . . . . . . . . . . .FIR Filters Defined in the Frequency Domain . . . . . . . .Comparison of Time-Domain (Impulse Response) andFrequency-Domain (FFT) Implementations for FIR Filtering . . . . . .Simulation of Filtering with IIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . .4.1.3.1.4.1.3.2.Systems Characterized by Linear Constant-Coefficient DifferenceEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Structures of Recursive Discrete Filters Implemented in SimulationModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1.3.2.1.4.1.3.2.2.4.1.3.2.3.Direct-Form (Canonic) Realization. . . . . . . . . . . . . . . . . . .The Cascade Interconnections of Biquadratic CanonicSections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Parallel Realization . . . . . . . . . . . . . . . . . . . . .4.1.3.3. Transformations between Continuous-Time and Discrete-Time SystemsRepresented by Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1.3.3.1.4.1.3.3.2.4.1.3.3.3.4.1.3.3.4.Impulse-Invariant Transformation. . . . . . . . . . . . . . . .The Bilinear Transformation. . . . . . . . . . . . . . . . . . .Effect of Mapping on Lowpass-Equivalent FiltersRepresented by Rational Functions. . . . . . . . . . . . . . .Guide for Mapping Recursive Filters Specified inFrequency Domain . . . . . . . . . . . . . . . . . . . . . . . .Effects of Finite Word Length in Simulation of Digital Filters . . . . . . . . . . .4.1.4.1.4.1.4.2.4.1.4.3.Roundoff Noise in Simulations of IIR Filters. . . . . . . . . . . . . . . .Roundoff Noise in Simulations of FIR Filters . . . . . . . . . . . . . . .Effects of Quantization in Computation of the Fast FourierTransform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133134135136141142145145149149149150152153154155156158158159159159162165165166166168169169170173178178181181182182Contents xv4.1.5. Summary of the Process of Mapping Continuous Signals and Systemsinto Discrete Signals and Systems for Simulation . . . . . . . . . . . . . . . . . . .4.1.5.1.4.1.5.2.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A Guide to the Selection of the Proper Method of Filter Simulation. .4.2.4.3.4.4.Time-Varying Linear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2.1.4.2.2.4.2.3.4.2.4.4.2.5.Examples of Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . .Time-Domain Description for Linear Time-Varying Systems . . . . . . . . . . . .4.2.2.1.4.2.2.2.The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Superposition Integral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Frequency-Domain Representations of Time-Varying Systems . . . . . . . . . . .4.2.3.1.4.2.3.2.4.2.3.3.Two-Dimensional Frequency Response . . . . . . . . . . . . . . . . . . .Bandwidth Relations in Time-Varying Systems . . . . . . . . . . . . . .Sampling Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Properties of Linear Time-Varying Systems. . . . . . . . . . . . . . . . . . . . . . .4.2.4.1.4.2.4.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Interconnections of Linear Time-Varying Systems. . . . . . . . . . . . . . . .Models for LTV Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2.5.1.4.2.5.2.4.2.5.3.Linear Differential Equation with Time-Varying Coefficients . . . . . .Separable Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Tapped Delay-Line Channel Models . . . . . . . . . . . . . . . . . . . . .Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Appendix: Biquadratic Factors for Classical Filters . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 5. Modeling and Simulation of Nonlinear Systems5.1.5.2.5.3.Modeling Considerations for Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . .Memoryless Nonlinearities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.1.5.2.2.5.2.3.5.2.4.Memoryless Baseband Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . .Estimating the Sampling Rate for Nonlinear Systems. . . . . . . . . . . . . . . . .Memoryless Bandpass Nonlinearities: Analytically Based Models . . . . . . . . .5.2.3.1.5.2.3.2.The Limiter Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Power Series Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Memoryless Bandpass Amplifiers: Empirically Based Models . . . . . . . . . . .5.2.4.1.5.2.4.2.5.2.4.3.5.2.4.4.5.2.4.5.Description and Interpretation of AM/AM and AM/PMCharacteristics for Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Lowpass Equivalent of a Bandpass Amplifier . . . . . . . . . . . . . . .Alternative Approaches to Defining AM/AM and AM/PMCharacteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multiple Carriers and Intel-modulation Products . . . . . . . . . . . . . .Setting the Operating Point of a Memoryless Nonlinearity. . . . . . . .Nonlinearities with Memory (NLWM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1.5.3.2.NLWM Modeling I: Fitting Swept-Tone AM/AM and AM/PMMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1.1.5.3.1.2.5.3.1.3.The PozaSarokozyBerger (PSB) Model. . . . . . . . . . . . . . . . . .5.3.1.1.1.5.3.1.1.2.5.3.1.1.3.AM/AM Characteristics . . . . . . . . . . . . . . . . . . . . .AM/PM Characteristics . . . . . . . . . . . . . . . . . . . . .Combined Model . . . . . . . . . . . . . . . . . . . . . . . . .The Saleh Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Abuelmaatti Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NLWM Modeling II: Fitting Preset Structures . . . . . . . . . . . . . . . . . . . . .182182183184185186186187188189189190190190190192192193195196198201204206206207209212214215218219220221223224227227227229229229232234xvi Contents5.3.2.1.5.3.2.2.One FilterOne Nonlinearity (Two-Box) Models. . . . . . . . . . . . . .5.3.2.1.1.5.3.2.1.2.5.3.2.1.3.5.3.2.1.4.FilterNonlinearity with Least-Squares Fit . . . . . . . . . .FilterNonlinearity ARMA Model. . . . . . . . . . . . . . . . . .FilterNonlinearity with Small-Signal Transfer Function. . .NonlinearityFilter with Least-Squares Fit . . . . . . . . . .FilterNonlinearityFilter (Three-Box) Models. . . . . . . . . . . . . . .5.3.2.2.1.5.3.2.2.2.Three-Box Model with Least-Squares Fit . . . . . . . . . . .Three-Box Model with Specified Characteristics. . . . . . .5.3.3.5.3.4.5.3.5.NLWM Modeling III: Analytical Models . . . . . . . . . . . . . . . . . . . . . . . .5.3.3.1.5.3.3.2.Volterra Series Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Polyspectral Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.3.2.1.5.3.3.2.2.NonlinearityFilter Polyspectral Model . . . . . . . . . . . .FilterNonlinearity Polyspectral Model . . . . . . . . . . . .NLWM Modeling IV: Miscellaneous Models. . . . . . . . . . . . . . . . . . . . . .5.3.4.1.5.3.4.2.5.3.4.3.Power-Dependent Transfer Function Model. . . . . . . . . . . . . . . . . . . .Nonlinear Parametric Discrete-Time Models . . . . . . . . . . . . . . . .Instantaneous Frequency Model. . . . . . . . . . . . . . . . . . . . . . . .Setting the Operating Point for a Nonlinearity with Memory . . . . . . . . . . . .5.4.5.5.5.6.Nonlinear Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.1.5.4.2.5.4.3.5.4.4.5.4.5.Outline of Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Families of Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.2.1.5.4.2.2.Solution Using Explicit Methods . . . . . . . . . . . . . . . . . . . . . . .Solution Using Implicit Methods . . . . . . . . . . . . . . . . . . . . . . .5.4.2.2.1.5.4.2.2.2.Iterated PredictorCorrector Method. . . . . . . . . . . . . . . . .Root Finding Using NewtonRaphson Method . . . . . . .Properties of Numerical Methods: Accuracy and Stability . . . . . . . . . . . . . .5.4.3.1.5.4.3.2.Order of a Method: Computation of Local or Truncation Error. . . . . . .Absolute Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Computational Considerations: Methods of Quality Control . . . . . . . . . . . . . . . .Application of Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.5.1.5.4.5.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Stand-Alone Model for a Traveling-Wave Semiconductor Amplifier. . .Measurement Technique for Nonlinear Components . . . . . . . . . . . . . . . . . . . . . .5.5.1.5.5.2.5.5.3.The Vector Network Analyzer Single-Tone Measurement . . . . . . . . . . . . . .Dynamic AM/AM and AM/PM Measurement Techniques Using aPeriodically Modulated Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Time-Domain Measurement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .234234235235236236236237237237245246249252252253255256257257261263263263264266268269270271271272275275277280284285289291291291293294297297Chapter 6. Fundamentals of Random Variables and Random Processesfor Simulation6.1.6.2.6.3.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.1.6.2.2.6.2.3.Basic Concepts, Definitions, and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.1.1.6.2.1.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Statistical Averages or Expected Values . . . . . . . . . . . . . . . . . . .Multidimensional Random Variables (Random Vectors) . . . . . . . . . . . . . . .Complex Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Univariate Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Contents xvii6.3.1. Univariate ModelsDiscrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3.1.1.6.3.1.2.6.3.1.3.6.3.1.4.Uniform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Binomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Negative Binomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Poisson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3.2. Univariate ModelsContinuous. . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3.2.1.6.3.2.2.6.3.2.3.6.3.2.4.6.3.2.5.6.3.2.6.6.3.2.7.6.3.2.8.6.3.2.9.Uniform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Gaussian (Normal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Gamma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Rayleigh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chi-Square. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Students t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Generalized Exponential. . . . . . . . . . . . . . . . . . . . . . . . . . . .6.4. Multivariate Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.4.1.6.4.2.Multinomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multivariate Gaussian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.4.2.1.6.4.2.2.Properties of the Multivariate Gaussian Distribution . . . . . . . . . . .Moments of Multivariate Gaussian pdf. . . . . . . . . . . . . . . . . . .6.5. Transformations (Functions) of Random Variables. . . . . . . . . . . . . . . . . . . . . . .6.5.1.6.5.2.6.5.3.Scalar-Valued Function of One Random Variable . . . . . . . . . . . . . . . . . . .6.5.1.1.6.5.1.2.Discrete Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Continuous Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Functions of Several Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.5.2.1.6.5.2.2.6.5.2.3.Special CaseLinear Transformation. . . . . . . . . . . . . . . . . . . .Sum of Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Order Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Nonlinear Transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.5.3.1.6.5.3.2.Moment-Based Techniques. . . . . . . . . . . . . . . . . . . . . . . . . .Monte Carlo Simulation Techniques . . . . . . . . . . . . . . . . . . . .6.6. Bounds and Approximations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.6.1.6.6.2.6.6.3.6.6.4.6.6.5.Chebyshevs Inequality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chernoff Bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Union Bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Central Limit Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Approximate Computation of Expected Values. . . . . . . . . . . . . . . . . . . . .6.6.5.1.6.6.5.2.6.6.5.3.Series Expansion Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Moments of Finite Sums of Random Variables. . . . . . . . . . . . . . .Quadrature Approximations . . . . . . . . . . . . . . . . . . . . . . . . . .6.7. Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.7.1.6.7.2.Basic Definitions and Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Methods of Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.7.2.1.6.7.2.2.6.7.2.3.6.7.2.4.Joint Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Analytical Description Using Random Variables . . . . . . . . . . . . . . . . .Average Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Two or More Random Processes. . . . . . . . . . . . . . . . . . . . . . .6.7.3. Stationarity, Time Averaging, and Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . .6.7.3.1.6.7.3.2.Time Averages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.7.4. Correlation and Power Spectral Density Function of Stationary RandomProcesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298298298299299300300301301302302303303304304304304305305308308310310310313313314315316316316317317318318320321321322323326326328328328329330331332333334xviii Contents6.7.4.1.6.7.4.2.6.7.4.3.6.7.4.4.6.7.4.5.Autocorrelation Function and Its Properties. . . . . . . . . . . . . . . . .Cross-Correlation Function and Its Properties . . . . . . . . . . . . . . .Power Spectral Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Lowpass and Bandpass Processes. . . . . . . . . . . . . . . . . . . . . . .Power and Bandwidth Calculations. . . . . . . . . . . . . . . . . . . . . .6.7.5.6.7.6.Cross-Power Spectral Density Function and Its Properties . . . . . . . . . . . . . .Power Spectral Density Functions of Random Sequences . . . . . . . . . . . . . .6.8.6.9.6.10.6.11.Random Process Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.8.1.6.8.2.6.8.3.6.8.4.6.8.5.Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.8.1.1.6.8.1.2.6.8.1.3.Independent Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Markov Sequences (First Order) . . . . . . . . . . . . . . . . . . . . . . .Autoregressive and Moving Average (ARMA) Sequences . . . . . . . .M-ary Digital Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.8.2.1.6.8.2.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Random Binary Waveform. . . . . . . . . . . . . . . . . . . . . . . . . . .Poisson Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Shot Noise and Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.8.4.1.6.8.4.2.Shot Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Gaussian Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.8.5.1.6.8.5.2.6.8.5.3.Definition of a Gaussian Process . . . . . . . . . . . . . . . . . . . . . . .Models of White and Bandlimited White Noise . . . . . . . . . . . . . .Quadrature Representation of Bandpass (Gaussian) Signals . . . . . . .Transformation of Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.9.1.6.9.2.6.9.3.6.9.4.Response of Linear Time-Invariant Causal (LTIVC) System. . . . . . . . . . . . .6.9.1.1.6.9.1.2.6.9.1.3.Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Probability Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mean, Autocorrelation, and Power Spectral Density Functions . . . . .Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Response of Nonlinear and Time-Varying Systems . . . . . . . . . . . . . . . . . .6.9.4.1.6.9.4.2.Nonlinear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sampling of Stationary Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.10.1.6.10.2.Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.10.1.1.6.10.1.2.6.10.1.3.6.10.1.4.Sampling of Lowpass Random Processes . . . . . . . . . . . . . . . . .Aliasing Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Sampling Rate for Simulations . . . . . . . . . . . . . . . . . . . . . . .Sampling of Bandpass Random Process . . . . . . . . . . . . . . . . . .Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.10.2.1.6.10.2.2.Uniform Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Nonuniform Quantizer . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 7. Monte Carlo Simulation and Generation of Random Numbers7.1. Principle of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.1.1.7.1.2.Definition of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . .Variations of Monte Carlo SimulationQuasianalyticalMonte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335335336337338338339340340340340342344344345346346346348350351352354357357357357357358360361361362362362362363365365366367368369369371371373Contents xix7.2.7.3.7.4.7.5.7.6.Random Number Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.2.1.7.2.2.7.2.3.Generation of Uniform Random Numbers . . . . . . . . . . . . . . . . . . . . . . .7.2.1.1.7.2.1.2.WichmanHill Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . .MarsagliaZaman Algorithm . . . . . . . . . . . . . . . . . . . . . . . . .Methods of Generating Random Numbers from an Arbitrary pdf . . . . . . . . . .7.2.2.1.7.2.2.2.7.2.2.3.7.2.2.4.Transform Method ( Analytical) . . . . . . . . . . . . . . . . . . . . . . . . . . . .Transform Method (Empirical) . . . . . . . . . . . . . . . . . . . . . . . .Transform Method for Discrete Random Variables . . . . . . . . . . . .Acceptance/Rejection Method of Generating Random Numbers . . . .Generating Gaussian Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.2.3.1.7.2.3.2.Sum-of-12 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Box Mller Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Generating Independent Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . .7.3.1.7.3.2.7.3.3.7.3.4.White Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Random Binary Sequences and Random Binary Waveforms . . . . . . . . . . . .Pseudorandom Binary Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M-ary Pseudo noise Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Generation of Correlated Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . .7.4.1.7.4.2.7.4.3.Correlated Gaussian Sequences: Scalar Case. . . . . . . . . . . . . . . . . . . . . . . .7.4.1.1.7.4.1.2.Autoregressive Moving Average (ARMA) Models. . . . . . . . . . . . .Spectral Factorization Method. . . . . . . . . . . . . . . . . . . . . . . . .Correlated Gaussian Vector Sequences . . . . . . . . . . . . . . . . . . . . . . . . .7.4.2.1.7.4.2.2.Special Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .General Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Correlated Non-Gaussian Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Testing of Random Number Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.5.1. Stationarity and Uncorrelatedness . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.5.1.1.7.5.1.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Durbin Watson Test for Correlation . . . . . . . . . . . . . . . . . . . . .7.5.2. Goodness-of-Fit Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 8. Modeling of Communication Systems: Transmitterand Receiver Subsystems8.1.8.2.8.3.8.4.8.5.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Information Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.2.1.8.2.2.Analog Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.2.1.1.8.2.1.2.8.2.1.3.8.2.1.4.Single Test Tone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multiple Test Tones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Filtered Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . .Stored Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . .Digital Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Formatting/Source Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.3.1.8.3.2.Analog-to-Digital (A/D) Conversion. . . . . . . . . . . . . . . . . . . . . . . . . . .On Simulating the FSC Subsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . .Digital Waveforms: Baseband Modulation (I) . . . . . . . . . . . . . . . . . . . . . . . . . .Line Coding: Baseband Modulation (II). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.5.1. Logical-to-Logical Mapping I: Binary Differential Encoding . . . . . . . . . . . .373374376376377377379380381383383383384384385386389392393393395397397398399400400400401402405406407411411412412413413413414414416417420420xx Contents8.5.2.8.5.3.8.5.4.8.5.5.8.5.6.8.5.7.8.5.8.8.5.9.Logical-to-Logical Mapping II: Correlative Coding . . . . . . . . . . . . . . . . . .Logical-to-Logical Mapping III: Miller Code. . . . . . . . . . . . . . . . . . . . . . . .Logical-to-Real Mapping I: Non-Return to Zero (NRZ) Binary Signaling . . . .Logical-to-Real Mapping II: NRZ M-ary Signaling (PAM) . . . . . . . . . . . . .Logical-to-Real Mapping III: Return-to-Zero (RZ) Binary Signaling. . . . . . . .Logical-to-Real Mapping IV: Biphase Signaling or Manchester Code . . . . . . .Logical-to-Real Mapping V: Miller Code or Delay Modulation. . . . . . . . . . . . . . .Logical-to-Real Mapping VI: Partial Response Signaling . . . . . . . . . . . . . .8.6.8.7.8.8.8.9.8.10.8.11.8.12.Channel Coding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.6.1.8.6.2.Computational Load for Block Coding/Decoding. . . . . . . . . . . . . . . . . . . . . . . .Computational Load for Convolutional Coding/Decoding . . . . . . . . . . . . . .Radiofrequency and Optical Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.7.1.8.7.2.8.7.3.8.7.4.8.7.5.Analog Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Digital Quadrature Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.7.2.1.8.7.2.2.QPSK: Differential Quaternary Phase-Shift-Keying (DQSK). . . .Multitone Modulation/OFDM. . . . . . . . . . . . . . . . . . . . . . . . .Continuous Phase Modulation CPFSK, MSK, GMSK . . . . . . . . . . . . . . . .8.7.3.1.8.7.3.2.8.7.3.3.8.7.3.4.Continuous Phase Modulation. . . . . . . . . . . . . . . . . . . . . . . . .Continuous-Phase Frequency-Shift-Keying . . . . . . . . . . . . . . . . .Minimum-Shift-Keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Gaussian Minimum-Shift-Keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Coded Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Modeling Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Demodulation and Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.8.1.8.8.2.Coherent Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Noncoherent Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.8.2.1.8.8.2.2.8.8.2.3.Amplitude Demodulation. . . . . . . . . . . . . . . . . . . . . . . . . . . .Discriminator Detection of PM/FM Signals . . . . . . . . . . . . . . . .PLL Demodulation of PM/FM Signals . . . . . . . . . . . . . . . . . . .Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.9.1.8.9.2.8.9.3.8.9.4.8.9.5.8.9.6.8.9.7.8.9.8.Filters for Spectral Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Filters for Pulse Shaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Linear Minimum MSE Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Filters for Minimizing Noise and Distortion . . . . . . . . . . . . . . . . . . . . . .Matched Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Adaptive Filtering ( Equalization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.9.6.1.8.9.6.2.8.9.6.3.Tap-Gain Adaptation for Minimizing MSE . . . . . . . . . . . . . . . . .Covariance Matrix Inversion Method. . . . . . . . . . . . . . . . . . . . .Simulation Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . .Filters Specified by Simple Functions in the Frequency Domain . . . . . . . . . .Tabular Filter for Masks and Measurements . . . . . . . . . . . . . . . . . . . . . .Multiplexing/Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.10.1. Issues in the Simulation of Multiple-Access Methods. . . . . . . . . . . . . . . . . . .8.10.1.1.8.10.1.2.8.10.1.3.8.10.1.4.SDMA and PDMA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .FDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .TDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CDMA (Spread Spectrum Techniques) . . . . . . . . . . . . . . . . . .Radiofrequency and Optical Carrier Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.11.1.8.11.2.Radiofrequency Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Optical Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.12.1. Approaches to Including Synchronization in Simulation . . . . . . . . . . . . . . .421421422423423423423425425428431433434435438439443443445446447449451455457460460461465467467468470471472474476479480481483484484484486487489491491492495498Contents xxi8.12.2.8.12.3.8.12.4.8.12.5.8.12.6.8.12.7.8.12.8.Hardwired Synchronization: Phase and Timing Bias . . . . . . . . . . . . . . . . .Synchronization Using an Equivalent Random Process Model . . . . . . . . . . .Carrier RecoveryBPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Timing RecoveryBPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Carrier RecoveryQPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Timing RecoveryQPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation of Feedback Loops: Application to the Phase-Locked Loop,Phase-Locked Demodulator, and Costas Loop . . . . . . . . . . . . . . . . . . . . .8.12.8.1.8.12.8.2.8.12.8.3.8.12.8.4.8.12.8.5.8.12.8.6.Modeling Considerations for the PLL . . . . . . . . . . . . . . . . . . . .Stand-Alone PLL Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Assembled PLL Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Phase-Locked Loop as a Phase Tracker . . . . . . . . . . . . . . . .The Phase-Locked Loop as an FM Demodulator . . . . . . . . . . . . .Effect of Delay on the Performance of the Assembled PLL Model. . .8.13.8.14.Calibration of Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.13.1.8.13.2.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Calibration of Signal-to-Noise Ratio or for Digital Si gnal i ng. . . . . . . .8.13.2.1.8.13.2.2.8.13.2.3.Signal Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Noise Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Calibrating Signal-to-Noise Ratio and . . . . . . . . . . . . . . . .Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 9. Communication Channels and Models9.1.9.2.Fading and Multipath Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.1.1.9.1.2.9.1.3.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Shadow Fading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Multipath Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.1.3.1.9.1.3.2.9.1.3.3.9.1.3.4.9.1.3.5.9.1.3.6.9.1.3.7.Lowpass-Equivalent Characterization of Multipath Channels . . . . . .Statistical Characterization of Multipath Channels. . . . . . . . . . . . . . . .Statistical Characterization of the Time-Variant Behavior. . . . . . . . . . .Statistical Characterization: The WSSUS Model. . . . . . . . . . . . . .9.1.3.4.1.9.1.3.4.2.9.1.3.4.3.The Delay Power Profile . . . . . . . . . . . . . . . . . . . . . . . .The Spaced-Frequency Correlation Function. . . . . . . . . . . .The Time-Varying Channel . . . . . . . . . . . . . . . . . . .Structural Models for Multipath Fading Channels . . . . . . . . . . . . .9.1.3.5.1.9.1.3.5.2.9.1.3.5.3.Diffuse Multipath Channel Model . . . . . . . . . . . . . . .Statistical Tap-Gain Models. . . . . . . . . . . . . . . . . . . . .Generation of Tap-Gain Processes . . . . . . . . . . . . . . .Indoor Wireless Channels . . . . . . . . . . . . . . . . . . . . . . . . . . .9.1.3.6.1.9.1.3.6.2.9.1.3.6.3Factory and Open-Plan-Building Model. . . . . . . . . . . .Office Building Model. . . . . . . . . . . . . . . . . . . . . . . .Ray-Tracing Prediction Model. . . . . . . . . . . . . . . . . . . .Radio-Relay Line-of-Sight (LOS) Discrete Multipath FadingChannel Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Almost Free-Space Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.2.1.9.2.2.9.2.3.Clear-Air Atmospheric (Troposphenc) Channel . . . . . . . . . . . . . . . . . . . .The Rainy-Atmospheric Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Ionospheric Phase Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .500502504506510513514514515522528529531534534535535538538539540546546547549550551551553554557558561561572575576577578582583586587587589xxii Contents9.3.9.4.9.5.9.6.9.7.Conducting and Guided Wave Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.3.1.9.3.2.Rectangular Waveguide Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Fiber Optic Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Finite-State Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.4.1.9.4.2.9.4.3.9.4.4.Finite-State Memoryless Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Finite-State Models with Memory: Hidden Markov Models ( HMM) . . . . . . . .9.4.2.1.9.4.2.2.9.4.2.3.N-State Markov Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .First-Order Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . .Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Types of Hidden Markov Models: Gilbert and Fritchman Model. . . . . . . . . . . .Estimation of the Parameters of a Markov Model. . . . . . . . . . . . . . . . . . . . .Methodology for Simulating Communication Systems Operating overFading Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.5.1.9.5.2.9.5.3.Waveform-Level Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Symbol-Level Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Speech Coder Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Appendix Reference Models for Mobile Channels . . . . . . . . . . . . . . . . . . . . . . .9.A.1.9.A.2.9.A.3.Reference Channel Models for GSM Applications . . . . . . . . . . . . . . . . . .Reference Models for PCS Applications . . . . . . . . . . . . . . . . . . . . . . . .Reference Channel Models for UMTS-IMT-2000 Applications. . . . . . . . . . . . . . .9.A.3.1.9.A.3.2.Path Loss Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.A.3.1.1.9.A.3.1.2.9.A.3.1.3.9.A.3.1.4.Path Loss Model for Indoor Office Test Environment. . .Path Loss Model for Outdoor-to-Indoor andPedestrian Test Environments . . . . . . . . . . . . . . . . .Path Loss Model for Vehicular Test Environments . . . .Decorrelation Length of the Long-Term Fading . . . . . .Channel Impulse Response Model . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 10. Estimation of Parameters in Simulation10.1.10.2.10.3.Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.1.1.10.1.2.10.1.3.Random Process Model: Stationarity and Ergodicity. . . . . . . . . . . . . . . . . . . .Basic Notation and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Quality of an Estimator: Bias, Variance, Confidence Interval,and Time Reliability Product. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.1.3.1.10.1.3.2.10.1.3.3.10.1.3.4.10.1.3.5.Bias of an Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . .Variance of an Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Confidence Interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .TimeReliability Product . . . . . . . . . . . . . . . . . . . . . . . . .Normalized Measures . . . . . . . . . . . . . . . . . . . . . . . . . . .Estimating the Average Level of a Waveform. . . . . . . . . . . . . . . . . . . . . . . . . .10.2.1.10.2.2.10.2.3.10.2.4.10.2.5.Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Expected (Mean) Value of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . .Variance of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mixture (Signal Plus Noise) Processes . . . . . . . . . . . . . . . . . . . . . . . .Confidence Interval Conditioned on the Signal. . . . . . . . . . . . . . . . . . . . . .Estimating the Average Power (Mean-Square Value) of a Waveform. . . . . . . . . . . . . . .10.3.1. Form of the Estimator for Average Power . . . . . . . . . . . . . . . . . . . . . .591591593596597599600601601604606610611612613613614614617618618618618618619619621626626626628628629629631631631631632632635635636637Contents xxiii10.3.2.10.3.3.Expected Value of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Variance of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.4.10.5.10.6.10.7.10.8.Estimating the Probability Density or Distribution Function of the Amplitudeof a Waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.4.1.10.4.2.The Empirical Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Empirical Probability Density FunctionHistogram . . . . . . . . . . . . .10.4.2.1.10.4.2.2.10.4.2.3.Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . .Expectation of the Estimator . . . . . . . . . . . . . . . . . . . . . . .Variance of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . .Estimating the Power Spectral Density (PSD) of a Process. . . . . . . . . . . . . . . . . . . . .10.5.1.10.5.2.10.5.3.10.5.4.10.5.5.Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.5.1.1.10.5.1.2.The Correlogram or Indirect Method . . . . . . . . . . . . . . . . . .The Periodogram or Direct Method . . . . . . . . . . . . . . . . . . .Modified Form of the Estimator: Windowing and Averaging. . . . . . . . . . . . . .Expected Value of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Variance of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Some Considerations on Implementing PSD Estimators: Summaryof the Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.5.5.1.10.5.5.2.Welch Periodogram Procedure (Direct Method) . . . . . . . . . . . . . . .Windowed Correlogram Procedure (Indirect Method) . . . . . . . .Estimating Delay and Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.6.1.10.6.2.10.6.3.Estimating Carrier Phase and Timing Synchronization in theNoiseless Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Block Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.6.2.1.10.6.2.2.Block Delay Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Block Phase Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Distribution of PLL-Based Phase and Timing Estimators . . . . . . . . . . . . .10.6.3.1.10.6.3.2.Distribution of the Phase Estimator . . . . . . . . . . . . . . . . . . . .Distribution of the Timing Estimator . . . . . . . . . . . . . . . . . . .Visual Indicators of Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.7.1.10.7.2.Eye Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Scatter Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 11. Estimation of Performance Measures from Simulation11.1.11.2.Estimation of Signal-to-Noise Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.1.1.11.1.2.11.1.3.11.1.4.Derivation of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Form of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Statistical Properties of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . .Implementing the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Estimating Performance Measures for Digital Systems . . . . . . . . . . . . . . . . . . . .11.2.1.11.2.2.11.2.3.Performance Characterization for Digital Systems and Run-TimeImplications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A Conceptual Framework for Performance Estimation. . . . . . . . . . . . . . . . . . .The Monte Carlo Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.3.111.2.3.2.11.2.3.3.Confidence Interval: Binomial Distribution . . . . . . . . . . . . . . .Confidence Interval: Poisson Approximation. . . . . . . . . . . . . . . . . . .Confidence Interval: Normal Approximation. . . . . . . . . . . . . . . . . . .637638640640641642643644645646646647648651652653653654655655657658660661662664664664666667667670670673673675678679683686688691691xxiv Contents11.2.3.4.11.2.3.5.11.2.3.6.11.2.3.7.Mean and Variance of the Monte Carlo Estimator . . . . . . . . . .Effect of Dependent Errors . . . . . . . . . . . . . . . . . . . . . . . .Sequential Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . .Estimation of Interval Measures . . . . . . . . . . . . . . . . . . . . .11.2.3.7.1.11.2.3.7.2.11.2.3.7.3.Using a Generative Model. . . . . . . . . . . . . . . . . . .Using a Descriptive Model . . . . . . . . . . . . . . . .Interval Simulation . . . . . . . . . . . . . . . . . . . . .11.2.4.11.2.5.11.2.6.11.2.7.Tail Extrapolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.4.1.11.2.4.2.11.2.4.3.11.2.4.4.Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . .Asymptotic Bias of the Estimator . . . . . . . . . . . . . . . . . . . .Variance of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . .Summary of the Simulation Procedure for Implementing TailExtrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.5.1.11.2.5.2.11.2.5.3.11.2.5.4.Formulating IS for Simulation Implementation . . . . . . . . . . . .Properties of the Importance Sampling Estimator. . . . . . . . . . . . . .Choosing Biasing Densities. . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.5.3.1.11.2.5.3.2.A Heuristic Approach . . . . . . . . . . . . . . . . . . .A Formal Approach. . . . . . . . . . . . . . . . . . . . .Stochastic Importance Sampling . . . . . . . . . . . . . . . . . . . . .Efficient Simulation Using Importance Splitting . . . . . . . . . . . . . . . . . .11.2.6.1.11.2.6.2.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Application of DPR-Based Splitting Simulation. . . . . . . . . . . . . . . .Quasianalytical (Semianalytic) Estimation . . . . . . . . . . . . . . . . . . . . . .11.2.7.111.2.7.2.11.2.7.3.11.2.7.4.11.2.7.5.11.2.7.6.11.2.7.7.11.2.7.8.11.2.7.9.General Scheme for the QA Method. . . . . . . . . . . . . . . . . . . . . .QA Method for Binary Systems . . . . . . . . . . . . . . . . . . . . .QA Method for Single-Dimensional Multiamplitude Modulation. . .QA Method for QAM Modulation. . . . . . . . . . . . . . . . . . . .QA Method for PSK Modulation . . . . . . . . . . . . . . . . . . . .QA Techniques for Coded Systems with Hard-DecisionDecoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.7.6.1.11.2.7.6.2.Independent-Error Channel . . . . . . . . . . . . . . . .Dependent-Error Channel . . . . . . . . . . . . . . . . .QA Method for Convolutionally Coded Systems withSoft-Decision Decoding . . . . . . . . . . . . . . . . . . . . . . . . . .Incorporating Jitter in the QA Technique . . . . . . . . . . . . . . . .Mixed QA Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 12. Four Case Studies12.1. Case Study I: 64-QAM Equalized Line-of-Sight Digital Radio Link in aFading Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.1.1.12.1.2.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.1.2.1.12.1.2.2.12.1.2.3.12.1.2.4.12.1.2.5.The Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Transmitted Signal . . . . . . . . . . . . . . . . . . . . . . . . . .The Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .694696697697698700701703706707707709710713717719719724732734734736737739740743744745748748751753753754757758763763765766767767769769Contents xxv12.1.2.6.12.1.2.7.12.1.2.8.12.1.2.9.12.1.2.10.Receiver Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Receiver Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .The Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.1.3.12.1.4.12.1.5.The Selected Channel Snapshot Simulation . . . . . . . . . . . . . . . . . . . . .12.1.3.1.12.1.3.2.12.1.3.3.12.1.3.4.Simulation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . .Estimation of Error Probability. . . . . . . . . . . . . . . . . . . . . . . . . . .Selected Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . .The Stochastic Channel Sequence Simulation. . . . . . . . . . . . . . . . . . . . . . . . .12.1.4.1.12.1.4.2.12.1.4.3.12.1.4.4.12.1.4.5.12.1.4.6.12.1.4.7.Stochastic Channel Sequence Generation. . . . . . . . . . . . . . . . . . . .Evaluation of Error Probability: Fast QuasianalyticalMethod 1 (FQA-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Evaluation of Error Probability: Fast QuasianalyticalMethod 2 (FQA-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Evaluation of Error Probability: The Moment Method(Gaussian Quadrature) . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Evaluation of the Outage Probability . . . . . . . . . . . . . . . . . .Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.2.12.3.12.4.Case Study II: Phase Noise and Its Effect on Block-Coded Systems. . . . . . . . . . . . . .12.2.1.12.2.2.12.2.3.12.2.4.12.2.5.12.2.6.12.2.7.12.2.8.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Analytical Formulation: Demodulated Signal . . . . . . . . . . . . . . . . . . . .Quadrupling Loop Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Residual Phase Noise Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.2.4.1.12.2.4.2.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Calibrating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . .Residual Phase Noise Random Number Generator . . . . . . . . . . . . . . . . .A Quasianalytical Generator for the Error Sequence . . . . . . . . . . . . . . . .Postprocessing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Case Study III: Exploring the Effects of Linear and Nonlinear Distortionsand Their Interactions on MSK-Modulated Signals: A Visual Approach. . . . . . . . . .12.3.1.12.3.2.12.3.3.12.3.4.12.3.5.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Linear Filter Distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.3.2.1.12.3.2.2.12.3.2.3.12.3.2.4.12.3.2.5.12.3.2.6.12.3.2.7.12.3.2.8.Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Bandlimiting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Linear Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Parabolic Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . .Parabolic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Cubic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Residual Amplitude and Phase . . . . . . . . . . . . . . . . . . . . . .Combined Effects of Linear Filter Distortions . . . . . . . . . . . . .Memoryless Nonlinear AM/AM and AM/PM Distortions . . . . . . . . . . . .Nonlinear Filter Distortions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Case Study IV: Performance Evaluation of a CDMA Cellular Radio System. . . . . . .12.4.1.12.4.2.12.4.3.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Brief Description of a CDMA Cellular System . . . . . . . . . . . . . . . . . . .Reverse Radio Link Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .770771773774777777777778779781782785786787787790791792793793793796798799799802803806807809809809812812814814816816817818818818820822822822825826xxvi Contents12.4.3.1.12.4.3.2.12.4.3.3.The Simulation Model of the Reverse Radio Link . . . . . . . . . .12.4.3.1.1.12.4.3.1.2.12.4.3.1.3.The Transmitter . . . . . . . . . . . . . . . . . . . . . . .The Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . .The Receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation Run-Length Requirement . . . . . . . . . . . . . . . . . .Simulation Runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.4.4.12.4.5.12.4.6.The Forward Radio Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.4.4.1.12.4.4.2.12.4.4.3.The Simulation Model of the Forward Radio L i n k . . . . . . . . . .12.4.4.1.1.12.4.4.1.2.The Transmitter . . . . . . . . . . . . . . . . . . . . . . .The Receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . .QA Performance Evaluation of the Forward Link in aBursty Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . .Simulation Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Finite-State Channel Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.4.5.1.12.4.5.2.12.4.5.3.12.4.5.4.12.4.5.5.HMM Parameter Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . .Discrete Channel Modeling . . . . . . . . . . . . . . . . . . . . . . . .12.4.5.2.1.12.4.5.2.2.The Reverse Link. . . . . . . . . . . . . . . . . . . . . . . .The Forward Link. . . . . . . . . . . . . . . . . . . . . . . .The Number of States . . . . . . . . . . . . . . . . . . . . . . . . . . .Probability Distribution of Error-Free Intervals . . . . . . . . . . . .Probability Distribution of the Number of Errors in a Block . . . .Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.5. Appendix: Simulation of the Tap-Gain Functions for a Rayleigh Fading Channel. . . . . .12A.1.12A.2.12A.3.12A.4.12A.5.12A.6.12A.7.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Estimation of the Sampling Rates and Expansion Rates . . . . . . . . . . . . . . . .The Channel Shaping Filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .FIR Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .IIR Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Comparison of IIR and FIR Filter Implementation . . . . . . . . . . . . . . . . .Sampling Rate Expansion and Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Problems and ProjectsChapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .AppendixesA.B.C.D.A Collection of Useful Results for the Error Probability of Digital Systems. . . . . . . . . . . .Gaussian Tail Probabilities Q(x) and an Approximation . . . . . . . . . . . . . . . . . . . . . .Coefficients of the Hermite Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Some Abscissas and Weights for Gaussian Quadrature Integration. . . . . . . . . . . . . . . . . . . .826826828829831831832832832833835836836837838838839839840840841845845845846846847847848848851854856863865868871873874879891893895Contents xxviiE. Chi-Square Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8978997KLVSDJHLQWHQWLRQDOO\OHIWEODQN1IntroductionThe complexity of communication and signal processing systems has grown considerablyduring the past decades. During the same time, the emergence of a variety of new technol-ogies such as fast and inexpensive hardware for digital signal processing, fiber optics, inte-grated optical devices, and monolithic microwave integrated circuits has had significantimpact on the implementation of communication systems. While the growth in complexity ofcommunication systems increases the time and effort required for analysis and design, theneed to insert new technologies into commercial products quickly requires that the design bedone in a timely, cost-effective, and effort-free manner. These demands can be met onlythrough the use of powerful computer-aided analysis and design tools.A large body of computer-aided techniques has been developed in recent years to assistin the process of modeling, analyzing, and designing communication systems (17). Thesecomputer-aided techniques fall into two categories: formula-based approaches, where thecomputer is used to evaluate complex formulas, and simulation-based approaches, where thecomputer is used to simulate the waveforms or signals that flow through the system. Thesecond approach, which involves waveform-level simulation (and often incorporatesanalytical techniques), is the subject of this book.Since performance evaluation and trade off studies are the central issues in the analysisand design of communication systems, we will focus on the use of simulation for evaluatingthe performance of analog and digital communication systems with the emphasis on digitalcommunication systems.1.1. Methods of Performance Evaluation1.1.1. IntroductionThe performance of communication systems can be evaluated using formula-basedcalculations, waveform-level simulation, or through hardware prototyping and measurements.(This classification is not meant to imply that the three methods are mutually exclusive;indeed, the best approach is often one that combines all three.)Formula-based techniques, which are based on simplified models, provide considerableinsight into the relationship between design parameters and system performance, and they areuseful in the early stages of the design for broadly exploring the design space. However,except for some idealized and oversimplified cases, it is extremely difficult to evaluate the12 Chapter 1performance of complex communication systems using analytical techniques alone with thedegree of accuracy needed for finer exploration of the design space.Performance evaluation based on measurements obtained from hardware prototypes ofdesigns is of course an accurate and credible method, and is useful during the later stages ofthe design when the design choices are limited to a small subset. This approach is in generalvery costly and time-consuming and not very flexible. It is clearly not feasible to use thisapproach during the earlier stage of the design cycle when the number of design alternativesmay be large.With simulation-based approaches to performance evaluation, systems can be modeledwith almost any level of detail desired (subject, of course, to certain limitations) and thedesign space can be explored more finely than is possible with formula-based approachesor measurements. With a simulation-based approach, one can combine mathematical andempirical models easily, and incorporate measured characteristics of devices and actualsignals into analysis and design. Simulated waveforms can also be used as test signals forverifying the functionality of hardware.Indeed, a simulation-based approach can be used to create a rapid prototyping envir-onment for analysis and design of communication and signal-processing systems, an envir-onment in which software models can be combined with hardware data and real signals toproduce designs that are timely, cost-effective, and error-free.The primary disadvantage of the simulation approach is the computational burden,which can be reduced by a careful choice of modeling and simulation techniques. Asubstantial part of this book is devoted to the topics of simulation models and simulationtechniques.1.1.2. Hierarchical ViewIn a broad sense, the term communication system might refer to a global commu-nication network, a geosynchronous communication satellite, a terrestrial microwave trans-mission system, or a built-in modem in a personal computer. A hierarchical view that is oftenused to describe communication systems is shown in Figure 1.1. The top level in thisrepresentation is a communication network, which is made up of communication nodes(processors) interconnected via communication links or transmission systems as representedin the layer below. A communication link is made up of elements like modulators, encoders,filters, amplifiers, decoders, and demodulators and other components which perform signalprocessing operations. These elements can be analog circuits, digital circuits, or an algorithmimplemented on a programmable digital signal processor (DSP). Details of these elements arerepresented in the bottom layer of the hierarchy shown in Figure 1.1.A variety of simulation techniques are used to evaluate the performance of the variouslayers in Figure 1.1. At the network level, the flow of packets and messages over the networkis simulated using an event-driven simulator, and performance measures such as networkthroughput, response time, and resource utilization are estimated as a function of networkparameters like processor speeds, buffer sizes at nodes, and link capacities. Network simu-lations are used to establish specifications for the processors, protocols, and the commu-nication links.Communication links deal with the transmission of information-bearing waveforms overdifferent types of communication channels (free space, cables, wires, optical fibers, etc.). Fordigital transmission systems, the performance of communication links is measured in terms ofbit error characteristics, and the bit error rate performance is estimated by simulating the flowIntroduction 3Figure 1.1. Hierarchical view of communication systems.of waveforms using models for functional blocks such as modulators, encoders, filters,amplifiers, and channels. Whereas network simulations are used to establish specifications forcommunication links, link-level si